To summarize, in this paper we have studied a macroscopic BEC stretching across cosmological
length scales as a potential CDM candidate. While there have been a number of attempts in
this direction earlier, what is new in our work is the observation that the quantum potential
of this BEC gives rise to the effect of an observed DE in the form of a cosmological constant
\(\Lambda \) . In fact, more intriguingly, we not only perceive a coveted unification of the CDM and
the DE, as they stem out of the same source, but also that the visible baryonic matter
content of the universe crucially backreacts on the metric to determine ultimately the
evolutionary profile of the cosmic dark sector. Note that the positivity and the smallness
of \(\Lambda \)  here can be attributed to the fact that the quantum potential for the given
wavefunction being treated as a classical potential (or part thereof) in a gravitational
formulation is itself positive. On the other hand, although simple physical considerations,
such as the positive-definiteness of the total energy density of the universe and the
squared BEC mass (\(m^2\) ), can assert the extent of the quantum backreaction (QB), the most
stringent bound on the corresponding parameter \(\epsilon \)  comes from the legitimate demand that
the BEC density should not exceed the total density of the universe at the present epoch.
As a by-product, albeit of considerable importance, the upper bound on \(\epsilon \)  enables us to
determine the lower bound on \(m\) . In particular, it is well-known that the preferred boson
mass in the BEC, that can prevent the formation of small-scale structures in CDM via the
uncertainty principle
[1]},
is \(m \sim 10^{-22}~eV\) . While the above stringent bound is found to be \(\, \epsilon \lesssim \mathcal {O}(10^{-1})\,\) , it is ensured thereby that the lower bound on \(m\)  is well within the
allowed mass range for the BEC (i.e. between \(10^{-22}\)  eV and \(10^{-32}\)  eV, the Hubble
value). Of course, on the whole, it must be pointed out here that it is the macroscopic
wavefunction of the BEC, and the specific form of that wavefunction considered here,
which have made it essential for all the above to work.
Nevertheless, we have not contemplated on any deviation from the spatial flatness
assumption, and have accepted the latter as an observational fact, while determining
the bound on the QB parameter \(\epsilon \) , or that on the BEC mass \(m\) . Moreover, we have not
looked into the detailed aspects of the BEC, specifically, what its constituent bosons
would be. Such an exploration is certainly worthy, from the point of view of deriving
the density profiles of the CDM and comparing the same with the galaxy rotation data.
Although there have already been some works in this direction
[2]},
assuming the CDM to be solely due to the BEC, ample scope remains for garnering more
evidence, once the effect of the quantum potential in emulating the DE, alongwith the
backreaction of other constituents (such as baryons), are brought into consideration.
